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Fractional Parts of Non-Integer Powers of Primes. II

Shubin, Andrei (2022) Fractional Parts of Non-Integer Powers of Primes. II. Quarterly Journal of Mathematics, 73 (1). pp. 277-310. ISSN 0033-5606. doi:10.1093/qmath/haab031.

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We continue to study the distribution of prime numbers p, satisfying the condition {p^α} ∈ I ⊂ [0;1), in arithmetic progressions. In the paper, we prove an analogue of Bombieri-Vinogradov theorem for 0 < α < 1/9 with the level of distribution θ = 2/5 − (3/5)α, which improves the previous result corresponding to θ ≤ 1/3.

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Additional Information:© The Author(s) 2021. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Received: 24 November 2020. Revision received: 26 May 2021. Accepted: 11 June 2021. Corrected and typeset: 28 June 2021. Published: 28 June 2021. I would like to thank M. A. Korolev and M. Radziwill for many helpful discussions and advice. I also thank the anonymous referee for the careful reading of the paper and for pointing out a mistake in the earlier version.
Issue or Number:1
Record Number:CaltechAUTHORS:20220322-742376000
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Official Citation:Andrei Shubin, Fractional Parts of Non-Integer Powers of Primes. II, The Quarterly Journal of Mathematics, Volume 73, Issue 1, March 2022, Pages 277–310,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114006
Deposited By: George Porter
Deposited On:23 Mar 2022 16:17
Last Modified:23 Mar 2022 16:17

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